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9 Conclusions If you are asking about the hypothesis that Dream was using modifications for the six streams in question, then the ender pearl barter probability was 3 x 10-10 to 3 × 10-9 depending on how you implement the stopping criterion; let's choose 10-10. The blaze rod probability was 3 x 10-8. Combining these two probabilities using Equation 2 gives 1.2 × 10-16, Adding in the correction (by multiplying) for 100,000 possible sets of 11 streams to investigate in 1,000 different ways gives a investigation gives 10-8 or a 1 in 100 million chance. That is, there is a 1 in 100 million chance that a livestream in the Minecraft speedrunning community got as lucky this year on two separate random modes as Dream did in these six streams. That is extraordinarily low, though not nearly as low (by a factor of 75000) as concluded by the MST Report (1 in 7.5 trillion). The main things that increased the probability are: 1) using a Barter Stopping criterion (factor of about 100) and 2) using 100 times as many livestreams and 10 times as high a p-hacking correction, for which I have provided specific justification. If you are asking about the hypothesis that Dream was using modifications for all eleven streams, the probabilities are much higher because the other five streams had more typical results. The ender pearl probability goes up to 3 x 10-4 and the blaze rod probability goes up to 10-6. Combining these gives 7 x 10-9 and adding the 10$ boost gives 0.7 or 1 in 2. Note that my corrections are designed for low p- values, so this may not be fully accurate, but this inaccuracy would not affect the conclusion that this case is completely consistent with expectations. That is, an investigation of all the similar Minecraft livestreams that picked a runner who had unusual luck in two different ways would produce results as unusual as Dream's in these 11 streams. Note that for speedrunners to reach high positions on the leaderboard requires excellent skill and luck. These answers are extremely different, which is unsurprising because the ender pearl and blaze rod success rate is very different between the first five and last six streams. How should you decide between the case with eleven streams and the case with six streams? It depends on what you think the probability is that Dream would make a modification at that point (as compared to any other point) without being influenced by the actual probabilities. It was a natural breaking point in the timeline of streams independent of the fact that it was probabilistically extremely different, which argues for the six-stream hypothesis. If you allow the streak of streams/runs to be any length up to N (instead of choosing 6 or 11 in advance), then another correction of N° should be included. Using N ~ 10 gives a corrected probability of 1 in 10 million . This does not account for the fact that "lucky streaks" should be treated somewhat differently which would increase the odds, potentially up to 1 in a million. So if you think "if Dream would have chosen to modify his numbers then this is the only place within the eleven stream set that Dream would have modified them", then you should lean toward the 1 in 100 million case. If you think Dream could have chosen to modify his numbers in between any stream, then these odds should come down substantially to 1 in a 10 million. If you think that if Dream modifying things, he would only have done it at the beginning of all eleven streams in question, then the data show no statistically significant evidence that Dream was modifying the probabilities, given that he was investigated after it was noticed that he was lucky. Since the eleven-stream probability is so much higher, even if you think that (independent of the prob- abilities calculated after seeing the streams) there is a 100-to-1 chance Dream modified before the final six streams instead of before all eleven streams, the six stream case provides a negligible correction and the prob- ability becomes just 1/100. That is, external evidence that the probabilities were modified at this specific point would be needed to produce a significant probability of cheating. Even in the worst case, the probabilities are not so extreme as to completely rule out any chance that Dream used the unmodified probabilities. If you have independent high-probability reasoning to suppose that the game was modified by Dream before his final six runs, then the low probability of that hypothesis even after correcting for other biases suggests an alternative explanation. There are reasonable explanations for Dream's ender pearl and blaze rod probability, potentially including extreme "luck", but the validity and probability of those explanations depend on explanations beyond the scope of this document. One alternative explanation is that Dream (intentionally or unintentionally) cheated, though I disagree that the situation suggests that this is an unavoidable conclusion. In any case, the conclusion of the MST Report that there is, at best, a 1 in 7.5 trillion chance that Dream did not cheat is to0 extreme for multiple reasons that have been discussed in this document. 9The MST Report computes this in a different way: choosing the number of 11-stream livestreamers and then choosen any of 11*(11+1)/2 subsets from these streams. In addition to the possible issues mentioned above, this correction is pretty strongly dependent on the somewhat arbitrary choice of 11 (which is potentially relevant to Dream, but may not be universal). I instead propose that you take consider all sets of consecutive livestreams of a certain length, which leads to a correction of the number of livestreams times the number of plausible lengths

PIGLIN ON HIS WAY TO TO GIVE DREAM HIS ENDER PEARL COLLECTION

When you rig a Minecraft mob vote by getting your impressionable fans to vote for the most useless and most easily forgettable mob so that your speedruns won't get affected by a newly added mob but later on you get exposed for cheating on your speedruns with solid proof so your efforts in rigging a Minecraft mob vote was all for nothing now that you are looked at as a lying cheater in the speedrunning community

My speedrun statistics and evidence are better than yours NO RUN HAIHA'HA! HEY MINECRAFI SAN Speatunning lam PEARL DATATABLE What about BLAZE DATATABLE WAH-HA! НА! НА!НА! Far ut All f he World Other... Data... Entity HA HA НА dream RM PAVRS 23 RM DAVSS24 ww ld Distriwted by eivenat Ps Sydita

11 Conclusion In our analysis, we were able to conclude the following statements: • The events that were observed on Dream's stream cannot be modeled by any sensible, conventional probability distribution. • After accounting for any contributors of bias, the likelihood of this occurring is still unfathomably small. • There are no circumstances in a natural setting in which bartering and blaze drops could be dependent or biased to any notable degree, much less a degree strong enough to produce this result. • There is no way to accidentally manipulate these values in real time during an RSG speedrun, nor any conceivable way to do it intentionally using only conventional methods. The only sensible conclusion that can be drawn after this analysis is that Dream's game was modified in order to manipulate the pearl barter and rod drop rates.

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About

Dream Speedrun Cheating Controversy refers to confirmed allegations of cheating made against Minecraft YouTuber and speedrunner Dream in October 2020 which were supported with convincing evidence in December 2020, with Dream's version 1.16 Minecraft speedrun record being removed. In May 2021, Dream admitted to cheating but claimed that he did so inadvertently.

Background

On October 19th, YouTuber^[1] Shell Guy posted a nine-minute video in which he accused popular Minecraft YouTuber, streamer and speedrunner Dream of modding the game to manipulate RNG in order to grant himself a faster time in the any% glitchless category of version 1.16 of Minecraft: Java Edition, which ultimately resulted in Dream achieving a 19-minute speedrun record which was at the time the 5th fastest time in the category. The video (currently unlisted) received over 200,000 views in two months.

In the video, Shell Guy claimed that Dream had likely modified his game to alter the barter success rate for Ender Pearls, an item necessary to finish the game which can be obtained by trading with Piglin mobs with a 4.73% chance.

On December 11th, 2020, Speedrun.com's Minecraft speedrun moderation team posted^[2] a 29-page paper containing extensive circumstantial evidence that Dream modified his copy of the game in order to manipulate drop rates of certain items. In addition to confirming Dream's abnormal success rate with Ender Pearls barter, the research also highlighted Dream's success with obtaining Blaze rods (extracts shown below).

Part II Data The raw data (and its sources) from which the following graphs were derived can be found in Appendix A. 4 Piglin Bartering Bartering Luck Dream - Illumina Expected 99.9%ile 50 40 30 20 10 100 200 300 Cumulative Gold Ingots Figure 1: Dream's pearl barters, charted alongside various comparisons. The 99.9th percentile line represents one-in-a-thousand luck, which is already quite unlikely-if not necessarily proof of anything. Cumulative Pearl Trades

Blaze Rod Drops Blaze Luck Dream Illumina Expected 99.9%ile 250 200 150 100 50 50 100 150 200 250 300 Cumulative Blaze Kills Figure 2: The same for blaze rod drops. Cumulative Rod Drops

Also on December 11th, 2020, Speedrun.com Minecraft moderator Geosquare uploaded^[3] a video summarizing the paper's contents. The video received nearly 1 million views on YouTube in three days.

On December 11th, 2020, Dream was stripped^[4] of his version 1.16 record (originally 5th fastest and at that time 16th fastest globally).

Developments

On December 11th, 2020, Dream^[5]^[6] made a series of tweets in which he responded to the run being removed by denying the accusations of cheating and announcing that he would be making a response video (screenshots shown below, left and right).

dream @dreamwastaken2 · Dec 11 000 My 1.16 run was just rejected after research due to it being "too unlikely to verify". A video was made by a head mod and Youtuber Geosquare, using my name and clickbaiting "Cheating Speedrunning" in order to get easy views. Definitely a response soon. Total BS! 6.7K 27 4.3K 155.2K dream 000 @dreamwastaken2 Replying to @dreamwastaken2 Currently have multiple moderators messaging me that they believe that the verdict was bias, and that they might quit the mod team. What kind of "investigation" was this? 5:25 PM · Dec 11, 2020 · Twitter Web App

dream @dreamwastaken2 · Dec 11 00 Just to clarify, my 1.15 (previous world record), 5th place time was not removed and is still verified. Just the 16th place 1.16 run was "not able to be verified". I'll make a video at some point regarding it, but for now MCC tomorrow :D 2.7K 27 1.2K 111K dream @dreamwastaken2 · Dec 11 Thank you for the totally unbiased, 2 month, 29 page "investigation" into whether a 16th place run had "too good luck", that was then made into a clickbait Youtube video by a head moderator (what a shocker) 3.9K E7 2.6K 137.5K

On December 12th, 2020, Dream^[7] made a Reddit post in which denied the allegations and stated that the statement that he "regularly deleted his mod contents" made in the video was false. On December 13th, Dream^[8] posted a link his modpack folder and a log list for mods loaded at the time of the speedrun in question.

Posted by u/dreamistaken Dream 2 days ago 25 S 29 30 26 31 5.7k Speedrun Removal - Dream There's a lot of posts here about my 1.16 speedrun time removal, and some people upset with my response on Twitter. Obviously, I didn't cheat in any way and I plan on making a video to address these things. However, it will take time for me to thoroughly and completely address it, as the accusations took two months for the mods to work on. It's not something I can throw together in a day, and is going to require a lot of my attention. To clear up misinformation though, my 1.15 record remains up and verified, and I was not banned from submitting runs. My 1.16 (16th place, but 5th place when I got it) run was unverified due to the seemingly incredible statistical odds that I could have had the luck that I did over a few day period. As I didn't cheat, I know that there's going to be a way to disprove the statistics, but again, I'm not a mathematician and I don't know how. I'm going to be most likely hiring multiple well renowned statisticians to look at the numbers, and most likely have a roll in my response. On top of that, most likely talking with Minecraft developers, as well as other prominent figures regarding it. I understand that the numbers presented look suspicious, because they are not numbers you would ever expect to see during a non-glitched series of speedruns. I don't disagree with that, but I do have doubts that these numbers are entirely accurate, and I have doubts about the mods intent to fairly investigate my side. As for addressing the physical side of "how" I may have cheated, I can completely and fully beyond a reasonable doubt prove that I did not use a mod or datapack during my speedruns, and how I can prove that will obviously be talked about in the video. It's not related to the statistics, but it does show that it is much much more likely that the statistics are off (or that there is some other contributing factor). As for the video made by Geosquare, there was certain bits of misleading information, like the lie that I said that I "delete my mod contents regularly" (something that was never said). It made it seem like I was not cooperating with the investigation. I fully cooperated and provided every file that was ever requested from me, and I will be making those files public at some point in the future. On top of that, it was stated that I am a mod developer, when I have never developed a mod in my life, and do not know how to develop a mod. I can also reasonably prove this, and I offered the mod team at multiple points all of my development related files so they can tell that I did not code anything related to Minecraft RNG. It was also stated that it made it suspicious that I had "Fabric API" loaded, without mentioning why I had it loaded. I had provided the information of why I had Fabric API downloaded well before any suspicion involving Fabric API was brought forward. I volunteered the information that I did in fact have Fabric API downloaded, as I had nothing to hide. The log files that they showed in the video were again, volunteered by myself, as I had nothing to hide.

Dream's Video Response

On December 23rd, 2020, Dream^[11] uploaded a 23-minute video response in which he presented an independent probability analysis supposedly performed by a practicing astrophysicist (video was later deleted by Dream, reupload shown below). The analysis concluded that the chance of Dream's getting a lucky Ender Pearl barter and Blaze Rod streak varied between 1 in 10 million and 1 in 100 million and not 1 in 7.5 trillion as stated in the analysis presented by the Minecraft speedrun moderation team. In the video, Dream denied all allegations of cheating.

I care more about defending my character than a dumb leaderboard position.

On the same day, Dream released^[12] a document containing the 19-page probability analysis (extracts below).

So if you think ”if Dream would have chosen to modify his numbers then this is the only place within the eleven stream set that Dream would have modified them”, then you should lean toward the 1 in 100 million case. If you think Dream could have chosen to modify his numbers in between any stream, then these odds should come down substantially to 1 in a 10 million. If you think that if Dream modifying things, he would only have done it at the beginning of all eleven streams in question, then the data show no statistically significant evidence that Dream was modifying the probabilities, given that he was investigated after it was noticed that he was lucky. […]
Even in the worst case, the probabilities are not so extreme as to completely rule out any chance that Dream used the unmodified probabilities. There are reasonable explanations for Dream’s ender pearl and blaze rod probability, potentially including extreme ”luck”, but the validity and probability of those explanations depend on explanations beyond the scope of this document. […] In any case, the conclusion of the MST Report that there is, at best, a 1 in 7.5 trillion chance that Dream did not cheat is too extreme for multiple reasons that have been discussed in this document.

Dream's Admission to Cheating

On May 30th, 2021, Dream admitted in a Pastebin^[13] post that he indeed had mods installed on his version of Minecraft 1.16, but was unaware of them at the time of his run. He explained that after the drama had subsided, he and his team discovered that mods installed in version 1.15 of the game which he used for challenge runs had crossed over into version 1.16, which caused the high drop rates of key items.

Online Reactions

In the days following the decision to remove Dream's record and the evidence uploads, the allegations became a popular subject of discussions both in the speedrunning community and the Minecraft community. On December 12th, 2020, speedrun YouTuber EZScape^[9] reviewed the allegations and the evidence during a livestream, later uploading the video to YouTube (shown below, left). On the same day, speedrunner DarkViperAU^[10] posted a video about the controversy (shown below, right).

[This video has been removed]

Additionally, memes about Dream having unbelievable luck gained popularity online, particularly in the form of GIF Captions.

Search Interest

External References

^[1] YouTube – [CONFIRMED] Did Dream FAKE His Minecraft Speedruns?

^[2] Mcspeedrun.com – Dream Investigation Credits

^[3] YouTube – Did Dream Fake His Speedruns – Official Moderator Analysis

^[4] Speedrun.com – Minecraft: Java Edition

^[5] Twitter – @1337523741757239299

^[6] Twitter – @dreamwastaken2

^[7] Twitter – @dreamwastaken2

^[8] Reddit – Speedrun Removal – Dream

^[9] YouTube – Are Dream’s Minecraft Speedruns Cheated? Feat. Geosquare

^[10] YouTube – World's Biggest Speedrunner Dream Is A Cheater

^[11] YouTube – World's Biggest Speedrunner Dream Is A Cheater

^[12] Google Drive – Critique of Dream Investigation Results

^[13] Pastebin – On Speedrunning

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9 Conclus HOLY F--- If you are asking then the ender eams in question, implement the bining these two ving) for 100,000 stopping criterion probabilities usin possible sets of 11 streams to investigate in 1,000 different ways gives a investigation gives 10-8 or a l in 100 million chance. That is, there is a 1 in 100 million chance that a livestream in the Minecraft speedrunning community got as lucky this year on two separate random modes as Dream did in these six streams. That is extraordinarily low, though not nearly as low (by a factor of 75000) as concluded by the MST Report (1 in 7.5 trillion). The main things that increased the probability are: 1) using a Barter Stopping criterion (factor of about 100) and 2) using 100 times as many livestreams and 10 times as high a p-hacking correction, for which I have provided specific justification. If you are asking about the hypothesis that Dream was using modifications for all eleven streams, the probabilities are much higher because the other five streams had more typical results. The ender pearl probability goes up to 3 x 10-4 and the blaze rod probability goes up to 10-. Combining these gives 7x 10-9 and adding the 10 boost gives 0.7 or 1 in 2. Note that my corrections are designed for low p- values, so this may not be fully accurate, but this inaccuracy would not affect the conclusion that this case is completely consistent with expectations. That is, an investigation of all the similar Minecraft livestreams that picked a runner who had unusual luck in two different ways would produce results as unusual as Dream's in these 11 streams. Note that for speedrunners to reach high positions on the leaderboard requires excellent skill and luck. These answers are extremely different, which is unsurprising because the ender pearl and blaze rod success rate is very different between the first five and last six streams. How should you decide between the case with eleven streams and the case with six streams? It depends on what you think the probability is that Dream would make a modification at that point (as compared to any other point) without being influenced by the actual probabilities. It was a natural breaking point in the timeline of streams independent of the fact that it was probabilistically extremely different, which argues for the six-stream hypothesis. If you allow the streak of streams/runs to be any length up to N (instead of choosing 6 or 11 in advance), then another correction of N° should be included. Using N - 10 gives a corrected probability of 1 in 10 million. This does not account for the fact that "lucky streaks" should be treated somewhat differently which would increase the odds, potentially up to 1 in a million. So if you think "if Dream would have chosen to modify his numbers then this is the only place within the eleven stream set that Dream would have modified them", then you should lean toward the 1 in 100 million case. If you think Dream could have chosen to modify his numbers in between any stream, then these odds should come down substantially to 1 in a 10 million. If you think that if Dream modifying things, he would only have done it at the beginning of all eleven streams in question, then the data show no statistically significant evidence that Dream was modifying the probabilities, given that he was investigated after it was noticed that he was lucky. Since the eleven-stream probability is so much higher, even if you think that (independent of the prob- abilities calculated after seeing the streams) there is a 100-to-1 chance Dream modified before the final six streams instead of before all eleven streams, the six stream case provides a negligible correction and the prob- ability becomes just 1/100. That is, external evidence that the probabilities were modified at this specific point would be needed to produce a significant probability of cheating. Even in the worst case, the probabilities are not so extreme as to completely rule out any chance that Dream used the unmodified probabilities. If you have independent high-probability reasoning to suppose that the game was modified by Dream before his final six runs, then the low probability of that hypothesis even after correcting for other biases suggests an alternative explanation. There are reasonable explanations for Dream's ender pearl and blaze rod probability, potentially including extreme "luck", but the validity and probability of those explanations depend on explanations beyond the scope of this document. One alternative explanation is that Dream (intentionally or unintentionally) cheated, though I disagree that the situation suggests that this is an unavoidable conclusion. In any case, the conclusion of the MST Report that there is, that have be GO QUTSIDE Itiple reasons trilli do "The MST 11*(11+1)/2 dependent on t choosen any of pretty strongly rsal). I instead cho ts of co iengflip.ena times the number of plausible lengths

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Dream Speedrun Cheating Controversy

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About

Background

Also on December 11th, 2020, Speedrun.com Minecraft moderator Geosquare uploaded^[3] a video summarizing the paper's contents. The video received nearly 1 million views on YouTube in three days.

On December 11th, 2020, Dream was stripped^[4] of his version 1.16 record (originally 5th fastest and at that time 16th fastest globally).